Warm-Up With your new neighbor, find: The ratio of people wearing glasses to those not wearing glasses in our class (not counting teachers) The ratio students wearing shoes with laces to students wearing shoes without laces The ratio of students wearing short sleeves (above elbow) to those wearing long sleeves (below elbow)

7.1 Notes Ratios and Proportions Today’s Objectives: 1. Students will be able to write ratios.   2. Students will be able to write and solve proportions.

Vocab a comparison of two quantities using division Ratio   Ratio  a comparison of two quantities using division ratio of a and b: a to b, a : b, or 𝑎 𝑏 (𝑏≠0) simplest form (reduce fractions)

Example 1 a) The number of students who participate in sports programs at Central High School is 520. The total number of students in the school is 1850. Find the athlete-to-student ratio to the nearest tenth.   b) The country with the longest school year is China, with 251 days. Find the ratio of school days to total days in a year for China to the nearest tenth. (Use 365 as the number of days in a year.)

Vocab used to compare three or more quantities   Extended Ratios  used to compare three or more quantities a : b : c means 3 ratios: a : b, b : c, a : c

Example 2 a) In ΔEFG, the ratio of the measures of the angles is 5:12:13. Find the measures of the angles. b) The ratios of the angles in ΔABC is 3:5:7. Find the measure of the angles.

Example 3 a. The ratio of the measures of the sides of a triangle is 4:5:7, and its perimeter is 160 centimeters. Find the measures of each side of the triangle. b. The ratio of the measures of the sides of a triangle is 4:7:11, and its perimeter is 3300 meters. What are the measures of the sides of the triangle? c. The ratio of the measures of the sides of a triangle is 5:6:9, and its perimeter is 280 feet. What are the measures of the sides of the triangle?

Vocab equation stating that two ratios are equal Ex: 𝑥 3 = 4 𝑐   Proportion equation stating that two ratios are equal Ex: 𝑥 3 = 4 𝑐  Cross Product Property To solve a proportion, cross multiply and set products equal to each other Ex: 𝑥 3 = 4 𝑐  𝑥 𝑐 =(4)(3)  Converse of the Cross Products Property  If ad = bc and 𝑏≠0 and 𝑑≠0, then 𝑎 𝑏 = 𝑐 𝑑

Example 4 Solve the following proportions. a) b) c)

Example 5 a) Monique randomly surveyed 30 students from her class and found that 18 had a dog or a cat for a pet. If there are 870 students in Monique’s school, predict the total number of students with a dog or a cat. b) Brittany randomly surveyed 50 students and found that 20 had a part-time job. If there are 810 students in Brittany's school, predict the total number of students with a part-time job.

Summary 1. You jog 3.6 miles in 30 minutes. At that rate, how long will it take you to jog 4.8 miles? 2. You earn $33 in 8 hours. At that rate, how much would you earn in 5 hours?  

Summary 3. An airplane flies 105 miles in ½ hour. How far can it fly in 1 ¼ hours at the same rate of speed? 4. What is the cost of six filters if eight filters cost $39.92? 5. If one gallon of paint covers 825 sq. ft., how much paint is needed to cover 2640 sq. ft.?

Summary A map scale designates 1” = 50 miles. If the distance between two towns on the map is 2.75 inches, how many miles must you drive to go from the first town to the second? Bob is taking his son to look at colleges. The first college they plan to visit is 150 miles from their home. In the first hour they drive at a rate of 60 mph. If they want to reach their destination in 2 ½ hours, what speed must they average for the remainder of their trip?

Summary  8. Four employees can wash 20 service vehicles in 5 hours. How long would it take 5 employees to wash the same number of vehicles?

Exit Slip Solve the proportion 9 2 = 27 2𝑦 2) In a triangle, the ratio of the measures of the sides is 2:3:4 and the perimeter is 72. Find the measures of the sides of the triangle.